An eligible L-2 spouse is generally employment-authorized incident to valid spousal status; the principal’s duties do not alter that separate rule.
Review every family member individually
Each dependant is assessed on their own facts. A spouse admitted in L-2 is employment-authorized incident to that status, so the authorization follows valid spousal status itself and does not depend on how the principal's duties are split or on where his employer is incorporated; employers generally accept the admission record as evidence of it. Children admitted in L-2 may attend school full time, but child status carries no work permission, and being paid by the family's own company does not change that.
Age is the hard edge, since derivative status depends on being unmarried and under 21, so a household with a child approaching that birthday should arrange the next status well ahead rather than discover the problem at an extension. Keep marriage certificates, birth certificates, passports and each person's own admission record together, because a derivative claim is proved by relationship documents and not by the principal's petition. Remote work for a Canadian employer performed from a U.S.
address is still work and should be assessed on its own before the household relies on that income. Derivative status is also only as sound as the principal's, which rests on the qualifying corporate relationship between two actively trading entities, one continuous year of full-time qualifying employment abroad within the preceding three years, a U.S. position that is primarily managerial or executive, and, for a new office, a first-year approval resting on real premises.
It ends when his ends, so a material change in his role reaches everyone in the file. Ask a U.S.-licensed immigration lawyer about a specific dependant before making a commitment.